
==== Front
J Gen PhysiolJ. Gen. PhysiolJ. Gen. PhysiolThe Journal of General Physiology0022-12951540-7748The Rockefeller University Press 9417141ArticleProperties of an Inwardly Rectifying ATP-sensitive K+ Channel in the 
Basolateral Membrane of Renal Proximal Tubule Mauerer Ulrich R. *Boulpaep Emile L. *Segal Alan S. *‡From the * Department of Cellular and Molecular Physiology, Yale University School of Medicine, New Haven, Connecticut 06520; 
and ‡ Department of Medicine, University of Vermont, Burlington, Vermont 05401Address correspondence to Alan S. Segal, Department of Medicine, 
University of Vermont, 55A South Park Drive, Colchester, VT 05446. 
Fax: 802-656-8915; E-mail: asegal@zoo.uvm.edu


1 1 1998 111 1 139 160 16 1 1997 30 10 1997 1998This article is distributed under the terms of an Attribution–Noncommercial–Share Alike–No Mirror Sites license for the first six months after the publication date (see http://www.rupress.org/terms). After six months it is available under a Creative Commons License (Attribution–Noncommercial–Share Alike 4.0 Unported license, as described at http://creativecommons.org/licenses/by-nc-sa/4.0/).The potassium conductance of the basolateral membrane (BLM) of proximal tubule cells is a critical 
regulator of transport since it is the major determinant of the negative cell membrane potential and is necessary 
for pump-leak coupling to the Na+,K+-ATPase pump. Despite this pivotal physiological role, the properties of this 
conductance have been incompletely characterized, in part due to difficulty gaining access to the BLM. We have 
investigated the properties of this BLM K+ conductance in dissociated, polarized Ambystoma proximal tubule cells. 
Nearly all seals made on Ambystoma cells contained inward rectifier K+ channels (γslope, in = 24.5 ± 0.6 pS, γchord, out = 
3.7 ± 0.4 pS). The rectification is mediated in part by internal Mg2+. The open probability of the channel increases modestly with hyperpolarization. The inward conducting properties are described by a saturating binding–unbinding model. The channel conducts Tl+ and K+, but there is no significant conductance for Na+, Rb+, 
Cs+, Li+, NH4
+, or Cl−. The channel is inhibited by barium and the sulfonylurea agent glibenclamide, but not by tetraethylammonium. Channel rundown typically occurs in the absence of ATP, but cytosolic addition of 0.2 mM 
ATP (or any hydrolyzable nucleoside triphosphate) sustains channel activity indefinitely. Phosphorylation processes alone fail to sustain channel activity. Higher doses of ATP (or other nucleoside triphosphates) reversibly inhibit the channel. The K+ channel opener diazoxide opens the channel in the presence of 0.2 mM ATP, but does 
not alleviate the inhibition of millimolar doses of ATP. We conclude that this K+ channel is the major ATP-sensitive basolateral K+ conductance in the proximal tubule.

ion channelkidneypatch-clampsulfonylureaepithelia
==== Body
introduction
The ability of the renal proximal tubule to maintain homeostatic electrolyte and water reabsorption in the face 
of drastic changes in dietary solute and water intake 
and renal hemodynamics implies that transtubular ion 
transport is tightly regulated. Proximal tubule potassium channels, particularly in the basolateral membrane (BLM),1 play pivotal physiologic roles in the regulation of membrane voltage, potassium recycling, and 
ultimately in transepithelial solute and water reabsorption. That the basolateral membrane potential of a 
proximal tubule cell is dominated by the BLM K conductance is well established (Sackin and Boulpaep, 
1983). The Na+,K+-ATPase pump in the BLM provides 
the energy that makes ion transport thermodynamically favorable, but continuous operation of the pump 
requires there be a K+ exit pathway. The BLM K conductance provides such a pathway and thus steady state 
intracellular K activity can be maintained in the face of 
large transcellular fluxes of salt and water (Sackin and 
Boulpaep, 1983). Since a major portion of the transcellular Na+ flux is reabsorbed across the BLM by the action of the Na+,K+-ATPase, a population of BLM K+ 
channels working in concert with the pump would allow K+ to recycle in a regulated fashion. Moreover, hyperpolarization secondary to the opening of BLM K+ 
channels enhances the driving force for electrogenic 
apical Na+ entry and basolateral Cl− efflux, resulting in 
net NaCl reabsorption.

The Ambystoma proximal tubule exhibits a large K+ 
conductance in the basolateral membrane (Siebens 
and Boron, 1987; Sackin and Boulpaep, 1981) that has 
been shown macroscopically to be sensitive to barium 
and pH. However, previous studies of the “macroscopic” BLM K+ conductance (Boulpaep, 1976) lack 
the resolution to distinguish whether there is one population of imperfectly selective K+ channels or a set of 
highly selective K+ channels coexisting with a population of nonselective cation channels. More recent “microscopic” single-channel patch-clamp studies of BLM 
K+ channels have shown diversity in both experimental 
design and findings (Tsuchiya et al., 1992; Hunter, 
1991; Parent et al., 1988; Kawahara et al., 1987; Sackin 
and Palmer, 1987; Gögelein and Greger, 1987a
, 1987b
), 
so a clear consensus has been elusive and details of the 
properties and regulation are lacking.

We have now characterized the properties and regulation (see Mauerer et al., 1998) of the principal K+ 
channel in the BLM in a preparation of dissociated yet 
polarized Ambystoma proximal tubule cells (Segal et al., 
1996). Inwardly rectifying, ATP-sensitive K+ channels 
were present in >95% of recordings from the BLM, 
each containing from 2 to >25 KATP channels/patch. 
Although the regulation of this proximal tubule BLM 
K+ channel is similar to that of recently cloned KATP 
channels in the apical membrane of the distal nephron 
(ROMK1 and ROMK2), there are important differences, and ROMK has not been found in the proximal 
tubule (Chepilko et al., 1995; Zhou et al., 1994; Lee 
and Hebert, 1995; Boim et al., 1995; Ho et al., 1993). 
The studies reported in this paper and the companion 
paper elucidate the properties and the regulation, respectively, of the major K+ channel underlying the 
BLM K conductance that is coupled to transport in the 
proximal tubule.

materials and methods
Solutions and Drugs
The compositions of the solutions used are summarized in Table 
I. After titration to pH 7.5 (710A; Orion Research, Boston, MA), 
sucrose was added to adjust the osmolality of the solutions (3MO; 
Advanced Instruments Inc., Needham Heights, MA). To determine channel conductance as a function of [K+], sucrose was 
added to the standard pipette KCl to maintain osmolality. Chemicals used were of the highest quality and obtained from Sigma 
Chemical Co. (St. Louis, MO), except thallium acetate (Aldrich 
Chemical Co., Milwaukee, WI), diazoxide (Calbiochem Corp., La 
Jolla, CA), ATPγS, and ADP (Boehringer-Mannheim Biochemicals, Indianapolis, IN). Nucleotides were prepared fresh daily as 
20–50-mM stocks in bath solution. Glibenclamide was dissolved 
in DMSO (100 mM stock).


Cell Preparation
Dissociated proximal tubule cells were isolated from amphibian 
kidneys as previously described (Segal et al., 1996). Briefly, 
aquatic phase Ambystoma tigrinum kept at 4°C were killed by submersion in 0.2% tricaine methanesulfonate. The kidneys were 
rapidly removed and placed in iced HEPES-buffered NaCl at pH 
7.5 (solution a). The adventitial tissue was removed by hand dissection, and the renal tissue was cut into 1–2 mm3 pieces and incubated in collagenase-dispase (0.2 U/ml of collagenase; Boehringer-Mannheim Biochemicals) on a gyratory shaker for 60 min 
at 22°C. The enzyme reaction was stopped by washing with Ca2+- 
and Mg2+-free NaCl (solution b
). The cells were then mechanically dispersed into suspension by repeated trituration, and a pellet was obtained by centrifugation at ∼1,600 rpm for 3 min. Finally, the cells were resuspended in 2.5 ml NaCl (solution a) in a 
35-mm culture dish, and stored at 4°C until use. The dissociated 
proximal tubule cells can retain their epithelial polarity for up to 
14 d (Segal et al., 1996). Cells were used for experiments from 2 
to 12 d after dissociation. Representative cells as seen under light 
microscopy (Fig. 1
A) and scanning electron microscopy (Fig. 1
B) are shown (for details of methods see Segal et al., 1996).


Electrophysiology
 A 5-μl aliquot of cell suspension in NaCl storage solution (solution a) was placed on a Cell-Tak™-coated glass coverslip in a recording chamber of our design (RC-5/25; Warner Instruments, 
Hamden, CT) mounted on an inverted microscope (Olympus 
IM; Olympus America, Inc., Melville, NY). The chamber has a 
bath volume of 500 μl, and solutions are perfused directly into an 
input multiplexer on the chamber at a gravity-driven flow rate of 
∼10 ml/min. 

Nonadherent cells were washed off the coverslip with the recording solution (either Ca2+-free NaCl, solution c, or KCl, solution d, unless otherwise noted) and the cells were visualized under Hoffman modulation optics (Modulation Optics, Greenvale, 
NY). Proximal tubule cells were readily recognized by their characteristic morphology (see Fig. 1; Segal et al., 1996). An individual proximal tubule cell was selected for an experiment only if it 
fulfilled the following criteria (Segal et al., 1996): (a) distinctly 
bilobated structure, (b) clearly defined brush border sharply delimited on the apical surface, (c) relatively smooth appearing basolateral membrane, and (d) absence of large vacuoles. 

Patch clamp.
The standard configurations for single-channel 
and whole-cell tight seal patch-clamp technique (Hamill et al., 
1981) were used to record channel currents from the BLM. Patch 
pipettes were fabricated from borosilicate glass capillaries (Warner 
Instruments, Hamden, CT) on a two-step puller (PP-83; Narishige 
Co., Ltd, Tokyo, Japan), coated with Sylgard 184™ (Dow-Corning 
Corp., Midland, MI) to within 200 μm of the tip, and fire-polished 
just before use. When filled with KCl, the open tip pipette resistance was 3–8 MΩ when placed in the initial bath solution. A hydraulic micromanipulator (Narishige) was used to guide the patch 
microelectrode to the BLM of the cell. High resistance giga-ohm 
seals (up to 50 GΩ) were obtained on the BLM in ∼75% of attempts by applying gentle suction to the pipette just after it 
touched the cell membrane. To achieve the whole-cell configuration, further suction was applied to rupture the cell-attached 
patch. Data have not been corrected for liquid-junction potentials since for most solutions they were <4 mV when measured as 
follows: the bath Ag-AgCl ground electrode was connected to the 
control KCl bath through a 3% agar bridge made of KCl pipette 
solution. A low resistance (<1 MΩ) pipette filled with 3 M KCl 
was placed in a KCl bath and the DC offset was adjusted to 0 mV 
in zero current clamp. The liquid-junction potentials were measured as the voltage offset resulting when the control KCl bath 
was replaced by the test solution. Low [Cl] solutions in which 
90% of Cl− was replaced by aspartate− had a liquid-junction potential of 13.3 mV.

 Voltage-clamped membrane currents were amplified (and 
zero current-clamp membrane potentials were measured) with 
an EPC-7 patch-clamp amplifier (Medical Systems, Greenvale, NY) 
controlled by a PDP 11/23 computer (Digital Equipment Corp., 
Maynard, MA). The current (filtered at 10 kHz) and voltage outputs of the EPC-7 were digitized at 44.1 kHz using a modified 
pulse code modulator (501ES; Sony Corp., Tokyo, Japan), and 
stored on videotape (SL-HF300; Sony Corp.). Whole-cell membrane currents were also digitized at 250 samples/s (Cheshire A/D; 
Indec, Sunnyvale, CA) and stored directly on computer disk. Signals were monitored on an oscilloscope (205; Hameg Instruments, Inc., Frankfurt, Germany) and strip-chart recorder (220; 
Brush, Cleveland, OH). All experiments were carried out at 
room temperature (20–22°C).

Data Analysis
Current data were played back and low pass filtered at 400 Hz 
(902LPF eight-pole Bessel filter; Frequency Devices Inc., Haverhill, MA), digitized at 1,000 samples/s, and stored on the PDP-11/
23. In some cases, currents were filtered at 40 Hz and digitized at 
100 samples/s for current binning and averaging analysis. Datafiles 
were transferred to a Pentium computer (Gateway 2000, North 
Sioux City, SD) via Kermit (Columbia University, NY) for analysis. 
Custom software for data acquisition and analysis was written in 
our laboratory using BASIC-23, AxoBASIC 1.0 (Axon Instruments, 
Foster City, CA), and Matlab 4.0 (The Mathworks, Natick, MA).

Channel activity (nP
o) was calculated over periods of 60–500 s 
as follows. The closed current level (i
c) was taken as the mode of 
the distribution around closed events. This current was subtracted from the current of a given bin, and the difference was 
multiplied by the number of events in that bin. The sum of these 
products yields the open channel area of the histogram. nP
o is 
given by dividing the open channel area by the single-channel 
current, i
sc. That is,
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\begin{equation*}nP_{o}=\frac{{ \,\substack{  \\ {\sum} \\ _{bins} }\, }[(i_{bin}-i_{c}){\cdot}({\mathit{No.\;events}}_{bin})]}{i_{sc}}.\end{equation*}\end{document} 


For kinetic analysis, currents were filtered at a corner frequency (f
c) of 2 kHz and sampled at 5,000 s−1. An event (transition) was counted each time a data point crossed the 50% level of 
the unitary channel current. For our recording system, the patch-clamp has a 5-kHz step response, a 5-kHz tape bandwidth, and a 
2-kHz eight-pole Bessel filter, yielding an effective bandwidth 
(−3 dB point, f
ceff) of 1.74 kHz. With these settings, the “dead 
time” of the recording system is given by Colquhoun and Sigworth (1983), Tdead = 0.179/f
ceff. The “50% delay time” of the 
Bessel filter is T50% = 0.506/f
c. For f
ceff = 1.74 kHz and f
c = 2 kHz, 
Tdead = 102.8 μs and T50% = 253 μs. Therefore, events in time histogram bins <500 s were cut off. Since an event lasting 253 μs would 
be the margin of detection, all dwell lifetimes <253 μs would be 
missed events. 

Open and closed dwell-time kinetics were fit to a probability 
density function expressed as a sum of exponentials,
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\begin{equation*}f(t)={ \,\substack{ ^{n} \\ {\sum} \\ _{i=1} }\, }\frac{A_{i}}{{\tau}_{i}}{\cdot}e^{-t/{\tau}_{i}},\end{equation*}\end{document} 


where n is the number of open or closed states, the Ai are the relative amplitudes, and the i are time constants. This function was 
transformed according to x = ln(t) and logarithmically binned 
(Sigworth and Sine, 1987), such that
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\begin{equation*}f(x)={ \,\substack{ ^{n} \\ {\sum} \\ _{i=1} }\, }A_{i}{\cdot}e^{\{(x-x_{i})-e^{(x-x_{i})}\}}.\end{equation*}\end{document} 


This function was used to fit the data using the Levenberg-Marquardt nonlinear least-squares fitting algorithm (Origin 4.0; Microcal Software, Inc., Northampton, MA) to find the appropriate 
set of τ's. Note that if the errors follow a Gaussian distribution, 
this nonlinear least-squares method is equivalent to the method 
of maximum likelihood (Colquhoun and Sigworth, 1983).

Dose–response relations for a drug (D) were fitted to the Hill 
equation as
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\begin{equation*}\frac{I}{I_{max}}=[1+ \left( \frac{K_{i}}{[D]} \right) ^{n_{H}}]^{-1},\end{equation*}\end{document} 


where I/I
max is the fractional inhibition, K
i is the concentration of 
drug giving 50% inhibition, [D] is the concentration of the drug, 
and n
H is the Hill coefficient. When n
H = 1, this equation reduces 
to the Langmuir adsorption isotherm.

In the text, the number of observations or experiments is reported, whereas n in the analysis denotes either the whole data 
set or the subset of total experiments in which precise quantitation could be reliably applied. In some figures, a running average 
(using a specified window width) of current versus time is displayed. Statistical values for the n elements are given as mean ± 
SEM. Student's t test was applied where appropriate.

results
Properties of the BLM K+ Channel
Overview.
With [K+] = 95 mM in the patch pipette, we 
found the K+ channel in 551 of 559 seals made on the 
BLM (98.6%). This K+ channel was never detected in 
seals made on the apical membrane (0 of 16, 0%), consistent with our previous finding that dissociated Ambystoma proximal tubule cells retain epithelial cell polarity (Segal et al., 1996). Seals on the BLM typically 
contained from 2 to >25 K+ channels. Despite numerous attempts to minimize patch area using small-tipped 
pipettes (resistance ≥ 30 MΩ), patches appearing to 
have one and only one channel were very infrequent 
(n = 4, only 0.7%). 

Cell-attached patches.
When cell-attached (c/a) patches 
were made in NaCl bath, spontaneous inward K+ currents were usually observed (95%) at 0 mV (−Vpip) 
command potential. By briefly switching to zero current clamp mode, the resting membrane potential 
(Vm) of the cell can sometimes be estimated if Rseal >> 
Rpatch. Using this method under these conditions, Vm 
averaged −37.2 ± 2.1 mV (n = 16), in good agreement 
with Vm = −40 mV as measured by conventional impalement (Segal et al., 1996). The Vm of the dissociated 
cells is ∼15–20 mV less than that for a cell in the intact 
tubule (Sackin and Boulpaep, 1983), suggesting an anion conductance exists at either the apical or basolateral membrane. Indeed, we have characterized a 
cAMP-activated Cl− channel in the BLM of these cells, 
which often appears in the same membrane patch as 
the K+ channel (not shown). Alternatively, the isolated 
cells may have acquired a nonspecific leak pathway that 
shunts the normally high K diffusion potential. Since 
the K+ and Cl− activity of the pipette solution (aP
K = 
0.80*[95] = 76 mM and aP
Cl = 0.78*[92] = 71.8 mM) 
is greater than the intracellular K+ and Cl− activity 
(ai
K = 0.80*[68] = 54.4 mM and ai
Cl = 0.78*[20.5] = 16 
mM (Sackin and Boulpaep, 1983), yielding a reversal potential (Erev) of −28.7 mV. Thus, at −Vpip = 0 mV, the inward current must be carried by K+ moving down its 
electrochemical gradient from the pipette into the cell.

Representative c/a current records at various command potentials are shown in Fig. 2
A, and the current–voltage (I-V) characteristic is shown in Fig. 2
B. 
The inward slope conductance is 22.2 ± 1.4 pS (taken 
from −40 to −80 mV, n = 8), and the outward slope 
conductance (from +20 to +80 mV) is 3.5 ± 0.1 pS 
(n = 5), and channel activity appears to increase with 
hyperpolarization (Fig. 2
A). Although the c/a I-V characteristic displays inward rectification, suggesting that 
the channel is an inward rectifier; under these conditions, the I-V relation would be expected to “inwardly 
rectify” due to Goldman-Hodgkin-Katz rectification. 


Excised patches.
When BLM membrane patches were 
excised in the inside-out (i/o) configuration into the 
standard bath solutions (solution c or d), channel activity typically began to decline and then disappear. Addition of 0.2 mM ATP to the bath before or just after 
patch excision prevented rundown and maintained 
channel activity indefinitely. 

Measurements of single-channel current with [K+] = 
95 mM on both sides of the membrane patch (plus 0.2 
mM ATP on the cytosolic side) demonstrate that the 
BLM K+ channel is a true inward rectifier (Fig. 3, A and 
B). The I-V relation in symmetrical [K+] inwardly rectifies and reverses very close to EK = 0 mV. The channel 
has an inward slope conductance of γslope, in = 24.5 ± 
0.6 pS (n = 8, measured between −60 and −100 mV), 
and an inward chord conductance of γchord, in = 20.5 ± 
0.4 pS (n = 8, measured between Erev = 0 and −100 
mV). The outward chord conductance measured at 
+80 mV is γchord, out = 3.7 ± 0.4 pS (n = 2). The outward slope conductance between +20 and +80 mV is 
clearly smaller.


Voltage dependence of nPo.
Since BLM membrane patches 
almost always contained more than one K+ channel, 
nP
o (channel activity) was used to assess the relative 
voltage dependence of P
o. This assumes that the number of active channel proteins in an excised patch remains constant as voltage varies. (We take n as the maximum number of simultaneously open channels observed, which places a minimum on the actual number 
of channel proteins in the patch.) As was the case for 
cell-attached patches, channel activity with KCl on both 
sides of the excised membrane patch increases with increasing hyperpolarization (Fig. 3
C). Although the absolute values of nP
o differed significantly among patches, 
relative nP
o increased e-fold per ∼83-mV hyperpolarization between −40 and −120 mV, reflecting a 27% 
increase of nP
o for every 20 mV of hyperpolarization.

Role of magnesium.
It has been shown that [Mg2+]i 
mediates at least part of the inward rectification in 
other inwardly rectifying K+ channels (Matsuda et al., 
1987; Horie et al., 1987; Ficker et al., 1994) by blocking 
outward currents in a voltage-dependent manner. 
When Mg2+
i was removed from the “cytosolic” side of i/o 
patches (solution e plus 0.2 mM Na2ATP), we observed 
flickering, and then rundown of the channel. This is in 
sharp contrast to the behavior of ROMK1 channels, in 
which channel rundown is slowed in a Mg2+-free bath 
(McNicholas et al., 1994). Since rundown occurs in the 
absence of free Mg2+
i and the presence of 0.2 mM 
Na2ATP (n = 4), it appears that at least the complex of 
Mg-ATP is required to prevent rundown. Interestingly, 
it has been shown that both Mg-ATP and free Mg2+
i are 
required to sustain channel activity for an ATP-insensitive inward rectifier K+ channel (Fakler et al., 1994). 
However, since higher levels of ATP block the BLM K+ 
channel (see below), it is not possible for us to dissociate the role of free Mg2+
i from that of the Mg-ATP complex. Millimolar concentrations of ATP (or indeed, any 
nucleotide) block the BLM K+ channel, and this effect 
is independent of both free Mg2+
i and Mg-ATP.

In a solution containing 368 nM Mg-ATP and 200 nM 
free [Mg2+]i (solution f ) (Fabiato and Fabiato, 1979), 
channel rundown did not occur. Although Fakler et al. 
(1994) showed that >10 μM free [Mg2+]i is required to 
prevent rundown from occurring in the Kir2.1 channel, 
just 200 nM free [Mg2+]i is sufficient for the BLM K+ 
channel. Under this condition, the outward unitary 
conductance of the latter increases, but the inward conductance is essentially unaffected. The enhanced outward current is ATP sensitive, as 5 mM ATP blocked 
89.3 ± 6.3% (n = 3) of the current. The outward chord 
conductance with [Mg2+]i = 200 nM increased from 
4.25 ± 0.59 pS to 14.4 ± 1.2 pS (n = 4, measured at 
+80 mV); inward currents were not affected by the 
change in [Mg2+]i (Fig. 3
B). Inward rectification was 
reestablished by returning bath [Mg2+]i to 1 mM.

Assuming a single-binding site, the Mg2+ block may 
be described using a one-site model according to 
Woodhull (1973):
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\begin{equation*}K(V_{c})=K(0mV){\cdot}exp(-{\delta}V_{c}zF/RT),\end{equation*}\end{document} 


where V
c is the command potential, z is the valence of 
2, and K(V
c) and K(0 mV) are the concentrations of 
Mg2+ causing half-maximal block at V
c and 0 mV, respectively. The factor δ may be the electrical distance of 
the binding site from the outside of the channel pore. 
Alternatively, δ can be considered together with another 
term to yield either the equivalent valence (z) of, or the 
effective potential (V
c) sensed by, the Mg2+ (Hille, 1992).

Current–voltage relations from inside-out patches in 
symmetrical K+ for several [Mg2+]i were constructed, 
from which the current was normalized to that observed in a Mg2+-free bath, and the relative current was 
plotted against command potential for each [Mg2+]i 
(not shown). These data were then fitted (nonlinear 
least squares fitting routine) by the following function 
that incorporates Eq. 5:
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\begin{equation*}\frac{I_{Mg^{2+}}}{I_{Mg^{2+}free}}=\frac{K(V_{c})}{K(V_{c})+[Mg^{2+}]}.\end{equation*}\end{document} 


The fit according to Eq. 6 yields the following results: 
δ = 0.57, K(0 mV) = 7.7 mM, K(60 mV) = 0.72 mM. 

Concentration and voltage dependence of isc.
To further investigate the biophysical properties of this channel, we 
asked the question of how varying extracellular [K+] 
would affect the current carried by the channel. To isolate the change in [K+] from any change in driving 
force across the patch, the same [KCl] was used in the 
pipette and bath, thus clamping Erev to 0 mV. This approach allowed us to measure the change in absolute 
conductance while maintaining a constant relative permeability (i.e., we varied the Goldman-Hodgkin-Katz 
current equation while holding the result of the Goldman-Hodgkin-Katz voltage equation constant). Under 
these conditions, the command potential is the only 
driving force for net K+ movement across the membrane patch. Pipette and bath [KCl] ranged from 5 to 
205 mM while osmolality was kept at 400 mosm/kg using sucrose as necessary. Since isc for [KCl] = 95 mM 
was the same in both standard KCl solution (solution d, 
200 mosm/kg) or 400 mosm/kg KCl solution, the tonicity change itself does not significantly alter the conducting properties of the channel.

Channel events (inward current) were analyzed at 
command potentials of −20, −40, −60, −80, and 
−100 mV for [K+] = 5, 10, 20, 25, 55, 95, 155, and 205 
mM, and the I-V relationship was determined for each 
of these KCl concentrations. Channel events for [K+] = 5 
mM could not be adequately resolved and were not 
included in the further analysis. For each voltage, the 
single channel current increases with [K+] and approaches a limiting current (i
max,sc). Similarly, the single channel chord conductance (γchord) also increases 
with [K+] and saturates (as shown for −100 mV in Fig. 
4
A). Fitting the γchord versus [K+] data at −100 mV 
with the Hill equation:
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\begin{equation*}{\gamma}={\gamma}_{max}{\cdot}[1+(K_{d}/[K^{+}]_{o})^{n_{H}}]^{-1}\end{equation*}\end{document} 


yielded a K
d of 77 mM, a Hill coefficient of 0.95, and a 
maximum value for γchord (γmax) of 36.6 pS (Fig. 4
A). 
Plots of γchord versus [K+] at different voltages yielded 
similar results for γmax. The average value for γmax determined at −60, −80, and −100 mV was 34.3 pS. 
γmax,sc was the same for all command potentials fitted. 
Indeed, the intersection of the channel's operating surface with the I-V plane as K shows a linear conductance. 
This mean value for γmax was applied to obtain K
d values and Hill coefficients for all the voltages (Table II).


Comparison of the dissociation constants K
d for the 
different command potentials shows that K
d decreases 
with hyperpolarization (Fig. 4
B and Table II). The relationship between K
d (mM) and voltage (mV) can be 
described by a single exponential decay
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\begin{equation*}K_{d}(V)=K_{d,{\infty}}+K_{d,0}{\cdot}exp \left( -\frac{V}{{\psi}} \right) =73+141{\cdot}exp \left( -\frac{V}{30} \right) \end{equation*}\end{document} 


where K
d, is the asymptotic value for K
d as Vpip → ∞•, K
d,0 
is the difference of K
d at the reversal potential (0 mV) 
and K
d,∞•. Finally, ψ is the voltage change required to effect an e-fold change in (K
d −K
d,∞•). 

Cation selectivity.
The cation to anion preference of 
the total BLM conductance was determined by salt dilution experiments using i/o membrane patches. Starting in symmetrical 95 mM K+ and 94.5 mM Cl− (EK = 
ECl = 0 mV) and holding at −Vpip = 0 mV, the bath was 
changed to a 14 mM K+ and 13.5 mM Cl− solution (solution i, EK = +48.6 mV, ECl = −49.4 mV) plus sucrose 
to maintain isoosmolality. This maneuver resulted in 
large inward currents (n = 3), reflecting the cation 
(K+) moving down its chemical gradient. The reversal 
potential for this membrane current (including leak) 
was at least +40 mV (n = 3). While holding at this E
rev, 
outward current developed when the 10% KCl bath was 
replaced with 100% KCl, due to K+ moving along its 
electrical gradient. Thus, the BLM conductance is cation selective.

Using the Goldman-Hodgkin-Katz voltage equation 
(Hodgkin and Katz, 1949; Goldman, 1943) for K+ and 
Cl−, the permeability ratio pK:pCl can be estimated (see 
materials and methods): 
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\begin{equation*}E_{rev}=\frac{RT}{F}ln\frac{p_{K}[K]_{o}+p_{Cl}[Cl]_{i}}{p_{K}[K]_{i}+p_{Cl}[Cl]_{o}}{\longleftrightarrow}\frac{p_{K}}{p_{Cl}}=\frac{exp \left( \frac{E_{rev}}{RT/F} \right) {\cdot}[Cl]_{o}-[Cl]_{i}}{[K]_{o}-exp \left( \frac{E_{rev}}{RT/F} \right) {\cdot}[K]_{i}}.\end{equation*}\end{document} 


where R = 8.315 J K−1 mol−1, F = 9.648 · 104 C mol−1, T 
= 293 K, E
rev ≥ +40 mV, [Cl]o = 94.5 mM, [K]o = 95 
mM, [Cl]i = 13.5 mM, and [K]i = 14 mM, yielding pK:
pCl of at least 17:1. Note that even a small change in E
rev 
to +44 mV would double the selectivity ratio. It is emphasized that this value represents the minimum cation 
to anion preference of the K+ channel since this is the 
selectivity ratio of the whole basolateral membrane 
patch including chloride and leak conductances.

Selectivity among cations.
Two approaches were used 
to determine the selectivity of this inwardly rectifying 
K+ conductance on the BLM. (a) Using c/a and i/o 
patches, the K+ in the patch pipette was replaced with 
the chloride salt of Na+ (n = 48), Rb+ (n = 4), Li+ 
(n = 4), Cs+ (n = 2), or NH1
4 (n = 7). Each solution 
was adjusted to pH 7.5 with the respective hydroxide salt. 
In all cases, c/a and i/o patches failed to show inward 
channel currents. These results strongly suggest that the 
BLM K+ channel is highly selective for K+ and excludes 
these cations, since channel activity is seen in >98% of 
seals made on the BLM when K+ is in the pipette. (b) 
Outside-out patches were made to exclude the remote 
possibility that the c/a and i/o patches used above did 
not contain any channels. The pipette was filled with 
KCl, and 0.2 mM Mg-ATP was included to prevent channel rundown. After recording in a KCl bath, the test 
cation was introduced into the bath (as the chloride 
salt) and the voltage protocol was repeated. KCl bath 
exchanges were interposed between test cations. 

The cation selectivity as determined from outside-out 
patches is exemplified in Fig. 5. For Na+ and Li+, the 
current at −40 mV is negligible, but a modest inward 
current is carried by Rb+, Cs+, and NH1
4. Exchanging 
the test cation with KCl returned the ensemble currents to the control level in all cases. That the outward 
current carried by K+ remains essentially unchanged 
during each bath cation substitution indicates that the 
test cations do not act as channel blockers from the 
outside. The ensemble current obtained at Vpip = −40 
mV shows that the selectivity of the channel for these 
cations is K+ >> Rb+ ≈ Cs+ ≈ NH4
+ > Na+ ≈ Li+. 


Thallium.
Many types of K+ channels have been 
shown not only to conduct Tl+, but often better than 
they conduct K+ (Hille, 1992). To assess the Tl+ conductance of the BLM K+ channel, the patch pipette was 
filled with 90 mM Tl-acetate (solution g ; the Cl salt of 
Tl+ was not used due to its low aqueous permeability) 
and the bath was filled with K-acetate (solution h). Under these conditions, inward Tl+ currents were observed in both c/a and i/o patches. The kinetic behavior of these channel events was notably different from 
those seen when the channel conducts K+. When conducting Tl+, the channel openings displayed more 
bursting, with each opening interrupted by fast flickery 
closures. The probability that this is actually a different 
channel is low since (a) the frequency of finding the K+ 
channel exceeds 98%, (b) other cation-selective channels were rarely observed, (c) the disparate kinetics 
were only seen when Tl+ was in the pipette, and (d) Tl+ 
currents were sensitive to glibenclamide (see below).

The I-V relationship for this biionic condition is 
shown in Fig. 3
B. The limiting inward slope conductance for Tl+ was 29.0 ± 1.0 pS (measured between 
−60 and −100 mV, n = 4). Thus the channel conductance is slightly higher for Tl+ than it is for K+ (g*inTl:
g*inK = 1.2:1). Since small inward currents were observed while holding at 0 mV in two i/o experiments 
with Tl+ in the pipette and K+ in the bath, the reversal 
potential is positive. This implies that the permeability 
(zero-current conductance) for Tl+ is also greater than 
that for K+. Therefore, compared with K+, Tl+ has a 
higher conductance and is more permeant but probably interacts with the pore, causing a fast channel block.

In conclusion, these findings indicate that the permeability sequence of this K+ channel is Tl+ > K+ >> 
Cs+ ≈ Rb+ ≈ NH4
+ > Li+ ≈ Na+ > Cl−.

Kinetics.
Due to the high density of this K+ channel 
in the BLM, a patch apparently containing only one 
channel is extremely rare. In over 550 seals, only four 
membrane patches appeared to contain only one channel (0.7%). Since the open probability (P
o) of the 
channel is only 0.05 ± 0.01 (n = 4), long recordings 
were required to accumulate enough transitions for 
meaningful analysis of the long closed state. Kinetic 
analyses from such patches show that under resting 
state conditions at −Vpip = −60 mV, the BLM K+ channel has two apparent open states and two apparent 
closed states. Parameters from one c/a patch and one 
i/o patch show that the open dwell lifetimes are (ms): 
τo1 = 0.78 (c/a), 1.21 (i/o), and τo2 = 4.7 (c/a), 6.6 (i/o). 
The closed dwell lifetimes are (ms): τc1 = 1.27 (c/a), 
0.72 (i/o), and τc2 = 397 (c/a), 502 (i/o). Fig. 6 shows 
the open and closed time histograms for a c/a patch.


Inhibitor Profile
The BLM K+ channel is inhibited by barium and glibenclamide. The channel is insensitive to tetraethylammonium (up to 10 mM) applied either to the extracellular or cytoplasmic side.

Barium.
We have previously shown by recording single-cell membrane potential that the whole cell conductance is dominated by a barium-sensitive K+ conductance (Segal et al., 1996). Perforated patch whole-cell recordings show that the barium-sensitive whole 
cell conductance inwardly rectifies. When 2 mM Ba2+ 
was included in the KCl pipette solution (unpaired experiments), channel openings were rare and a flickery 
state was noted. In contrast to the voltage dependence 
of channel activity without Ba2+ in the pipette (see Fig. 
3
C), steady depolarization now has the effect of increasing nP
o, and subsequent hyperpolarization reduced activity. This is presumably due to the voltage dependence of the Ba2+ block of the channel (data not 
shown). 

To quantify the Ba2+ block and use each patch as its 
own control, outside-out patches were made (n = 3). In 
outside-out membrane patches at −40 mV, Ba2+ inhibits the channel with a K
i = 460 μM (Fig. 7
A).


Glibenclamide.
This sulfonylurea is known to inhibit 
ATP-sensitive K+ channels in a number of epithelial tissues by binding to the sulfonylurea receptor (SUR). 
SUR1 has recently been cloned (Aguilar-Bryan et al., 
1995) and is thought to associate with the KATP channel, thereby conferring sulfonylurea sensitivity. However, SUR1 may not be present in the kidney (Inagaki 
et al., 1995), which may explain in part the much 
higher dose of glibenclamide required to inhibit renal 
KATP channels (Hebert and Ho, 1994). In this context, 
the BLM K+ channel is glibenclamide sensitive, albeit 
at “renal doses.” We treated 22 patches with glibenclamide; 16 excised inside-out patches were exposed to 
500 μM, while 6 cell-attached patches were exposed to 
low (0.01–10 μM) concentrations. In 7 of 16 inside-out 
patches, 500 μM glibenclamide inhibited activity by 
42.3 ± 5.6% (Fig. 7
B). Remarkably, the inhibition was 
much more potent in the cell-attached patches: 10 μM 
exerted an 83 ± 2% inhibition in three patches, and 
100 nM exerted a 70 ± 3% inhibition in three other 
patches (data not shown).

ATP Sensitivity
Similar to other KATP channels, low doses of ATP are required to prevent Ambystoma BLM K+ channel rundown, whereas millimolar doses inhibit channel activity. At a dose of 5 mM ATP, >90% of channel activity is 
inhibited. This effect is reversible as nP
o returns to 
baseline when the bath [ATP] is returned to 0.2 mM 
(Fig. 8
A). The dose–response curve for ATP has a K
i 
∼ 2.4 mM (Fig. 8
B). The Hill coefficient of ∼4 may 
suggest that the channel has a tetrameric structure, 
with each subunit possessing an ATP binding site. 
Thus, in the Ambystoma proximal tubule, the BLM K+ 
channel that appears to be the major K+ conductance 
of the cell is ATP sensitive.


Among the nucleoside diphosphates, ADP is less potent than ATP (ADP inhibits by 65.6 ± 8.1%, n = 4, P < 
0.01), but more potent than CDP, GDP, IDP, TDP, or 
UDP (data not shown). This suggests that the putative 
nucleotide binding site(s) recognize NDPs as well as 
NTPs, and that nucleotide hydrolysis is probably not 
occurring at this site. Indeed, even nucleoside monophosphates have a moderate inhibitory effect, although 
nucleosides themselves are without effect. The relative 
potency of the adenosine nucleosides (at 5 mM) in inhibiting the BLM KATP channel is ATP (93.3 ± 1.9%) > 
ADP (65.6 ± 8.1%) > AMP (38.7 ± 3.7%) > adenosine 
(1 ± 2%) (Fig. 8
C, n = 3–9).

Other nucleotides.
The effect of nucleotides was tested 
in excised i/o patches. All the NTPs tested reversibly inhibited BLM K+ channel activity at a dose of 5 mM 
(ATP 93.3 ± 1.9%, n = 9; CTP 70.3 ± 10.0%, n = 5; 
GTP 62.3 ± 7.5%, n = 3; ITP 61.1 ± 0.8%, n = 2; TTP 
53.7 ± 6.7%, n = 2; UTP 71.7 ± 5.7%, n = 2) (Fig. 8
C). These results suggest that each compound probably 
interacts with common cytoplasmic nucleotide binding 
site(s). Note that ATP is significantly more potent than 
the other nucleoside triphosphates (P < 0.02), but 
there is no significant difference among the nonadenosine nucleotides.

Rundown of the BLM K+ Channel
One characteristic of KATP channels is “rundown,” a 
gradual loss of activity when the membrane patch is deprived of cytosolic ATP (Findlay and Dunne, 1986). 
Typically, both Mg2+ and ATP are required to prevent 
rundown in KATP channels (Ashcroft and Ashcroft, 
1990). Likewise, the BLM K+ channel runs down in the 
absence of either Mg2+ or ATP (or both). Lower concentrations of ATP (100–200 μM) will prevent or “rescue” channel rundown. The experiment shown in Fig. 
9
A summarizes the characteristics of BLM K+ channel 
rundown. Channel activity typically begins to decrease 
(rundown) upon excision of the membrane patch into 
a nucleotide-free bath. If this process is allowed to continue, channel activity will cease, usually irreversibly. 
When 0.2 mM of ATP is added back, channel activity 
can be restored. When ATP is removed, all channels 
rapidly close. In the continued presence of ATP-γS, readdition of ATP is again able to rescue rundown, and 
activity returns to baseline upon washout of the ATP-γS. Frequently (but not invariably), ATP-γS has an inhibitory effect on single channel activity when added in 
the presence of ATP, which is reversible as long as the 
exposure is not prolonged (n = 6), as shown in Fig. 9
B. When ATP-γS is added in the absence of ATP, channel activity runs down very quickly, usually irreversibly 
(n = 4, data not shown).


Thus, ATP-γS cannot substitute for ATP in sustaining 
channel activity, suggesting that phosphorylation itself 
is not sufficient to prevent rundown. Although phosphorylation may be necessary, it appears that the nucleoside triphosphate must be hydrolyzable to maintain 
channel activity. This hypothesis is supported by the 
finding that CTP, GTP, ITP, TTP, and UTP could all 
prevent or rescue rundown, but the corresponding 
NDPs could not. Rescue does not appear to require the 
cAMP-dependent protein kinase, since channel activity 
can be restored even in the presence of a high concentration of protein kinase inhibitor (PKI, 1 μg/ml, P-0300; 
Sigma Chemical Co.).

Since it has been reported that removal of free Mg2+ 
nearly abolishes rundown of KATP in cultured CRI-G1 
insulin-secreting cells (Kozlowski and Ashford, 1990) 
and partially inhibits rundown of ATP-regulated 
ROMK1 channels excised in an ATP-free bath (McNicholas et al., 1994), we assessed BLM KATP channel activity 
under these conditions. The representative experiment 
shown in Fig. 9
C shows that rundown of the BLM KATP 
channel still occurs in the absence of ATP despite excision of the patch into a Mg2+-free bath.

Diazoxide.
The synthetic KATP channel opener diazoxide was applied to the cytoplasmic side of i/o patches. 
It has been shown that this benzothiadiazine can open 
KATP channels in the presence of Mg-ATP, but it may 
have an inhibitory effect in the absence of Mg-ATP (Kozlowski et al., 1989). Initial excision of the patch into an 
ATP-free bath leads to channel rundown as discussed 
above, and 200 μM diazoxide alone does not rescue 
rundown. However, addition of 0.2 mM Mg-ATP in the 
continued presence of, or after exposure to, diazoxide 
increases channel activity well in excess of that before 
rundown (n = 3, Fig. 10). The inhibitory effect of 5 
mM ATP is not diminished in the presence of, or by 
previous exposure to, diazoxide (n = 5, data not 
shown). 


Since low levels of Mg-ATP are required for diazoxide to open the BLM K+ channel, diazoxide probably 
does not interact with the rundown site. As hypothesized by others (Edwards and Weston, 1993, 1995), diazoxide may be acting at or near the nucleotide binding 
site that mediates inhibition. On the other hand, the 
interaction at this second site is more complex than a 
simple competition between the K channel opener and 
the nucleotide, since diazoxide does not relieve the inhibition by millimolar levels of ATP.

discussion
The proximal tubule (a leaky epithelium) can be considered to function within the general scheme of the 
epithelial transport model first proposed by Koefoed-Johnsen and Ussing (1958) (KJU), in which the apical 
membrane is primarily Na+ selective and the BLM is 
primarily K+ selective. Although this model was first applied to tight epithelia such as frog skin (Koefoed 
Johnsen and Ussing, 1958) and urinary bladder (Davis 
and Finn, 1982), its essence holds for leaky epithelia 
such as small intestine (Gunter-Smith et al., 1982) and 
the proximal tubule (Matsumura et al., 1984). In the 
KJU model, maintenance of unidirectional Na transport requires that K moves in a closed circuit (recycling) across the BLM. That is, barring intracellular accumulation of K (or K+ secretion), the K+ pumped into 
the cell by the pump must be matched by an outward 
K+ current across the BLM. 

Steady state vectorial transport in the proximal tubule thus requires continuous activity of the basolateral 
Na+,K+-ATPase pump, which consumes ATP and obligates intracellular accumulation of K+. A conductance 
for K+ is necessary both to allow this K+ to recycle and 
to maintain Vbl. Experiments performed by Matsumura 
et al. (1984) on perfused Necturus proximal tubules first 
demonstrated that the BLM GK varies as a function of 
pump activity, and they suggested that the regulation of 
BLM GK was linked to cellular metabolism, as had been 
previously proposed for red cells (Romero, 1978) and 
suspensions of rabbit cortical tubules (Balaban et al., 
1980). 

This hypothesis was bolstered when the first single-channel records of an ATP-sensitive K+ channel (K
i = 
0.1 mM) from cardiac muscle were published (Noma, 
1983). Similar ATP-sensitive K+ (KATP) channels were 
subsequently found in pancreatic β-islet cells (Cook 
and Hales, 1984), skeletal muscle (Spruce et al., 1985), 
and smooth muscle (Standen et al., 1989). The K
i for 
ATP is 10–100 μM for all these Type I KATP channels 
(Ashcroft and Ashcroft, 1990), and they are inhibited 
by sulfonylurea agents (Edwards and Weston, 1993). A 
KATP channel with these Type I properties has not been 
identified in epithelial tissues. However, a related KATP 
channel was recently demonstrated in nonperfused 
(Tsuchiya et al., 1992) and perfused (Hurst et al., 1993; 
Beck et al., 1993) rabbit proximal tubules. In preliminary experiments, we have also found this channel in 
the BLM of nonperfused rabbit proximal tubule, and 
in the present study we provide the first detailed description of the analogous BLM KATP channel in an amphibian using a novel preparation of dissociated proximal tubule cells that retain epithelial polarity (see Fig. 
1 and Segal et al., 1996).

Investigators have used several techniques to patch 
the BLM, including mechanically stripping off the 
basement membrane (Sackin and Palmer, 1987; Kawahara et al., 1987) and tearing tubules to access the lateral membrane (Gögelein and Greger, 1987b
). However, 
enzymatic treatment of nonperfused tubules (Tsuchiya 
et al., 1992; Parent et al., 1988), perfused tubules 
(Hurst et al., 1993; Beck et al., 1993), and single cells 
(Hunter, 1991) has been employed most commonly. 

We have previously shown that the dissociated Ambystoma proximal tubule cells (see Fig. 1) retain epithelial cell polarity (Segal et al., 1996). Indeed, the K+ 
channel described in the present study was present in 
>98% of seals made on the BLM, but was never detected in the apical membrane. With high [K] on both 
sides of the membrane patch, this BLM K+ channel exhibits inward rectification with γslope, in = 24.5 ± 0.6 pS 
and γchord, out = 3.7 ± 0.4 pS. This non-ohmic behavior 
in both cell-attached and -free membrane patches is 
due at least in part to a voltage-dependent open channel block by cytosolic Mg2+ (Matsuda et al., 1987). Removal of Mg2+ from the cytosolic side of i/o patches 
leads to an increase in outward conductance without affecting inward conductance. In c/a patches made on 
frog BLM (NaCl pipette in a KCl bath), Hunter (1991) 
estimated that the blocking site was 51.3% across the 
membrane from the cytosolic side (i.e., 0.513). This 
compares well to the value of 0.57 obtained for the Ambystoma BLM K+ channel in the present study. 

Inward rectification of current is not necessarily due 
to a decrease in the intrinsic outward conductance of 
the channel pore. Indeed, Matsuda et al. (1987) first 
described how ohmic single channel units could behave as rectifiers. They showed that inward rectification 
of a cardiac myocyte K+ channel was mediated by two 
effects: (a) Mg2+-independent voltage gating in which 
ohmic channels are open at hyperpolarized voltages 
and essentially inactivate upon depolarization, and (b) 
a Mg2+-induced voltage-dependent open channel (fast) 
block. Our data for the BLM K+ channel are in keeping 
with these observations since (a) the conductance is 
ohmic in the absence of cytosolic Mg2+, and (b) Mg2+ 
appears to cause a flickery open channel block of the 
outward current in the steady state (e.g., see Fig. 3
A). 
Naturally occurring polyamines (e.g., spermine) have 
also been shown to mediate inward rectification of 
some K+ channels (Ficker et al., 1994). However, spermine (up to 5 mM) does not affect the Ambystoma BLM 
K+ channel.

Properties of K+ conduction through the pore.
 Constant-field 
theory predicts that net K+ flux across the channel 
should increase linearly with rising [K+]. Most channels do not exhibit this behavior due to “competition” 
for binding sites within the pore, and saturation occurs 
at higher concentrations of the permeant ion (Hille, 
1992). In our study, conductance versus [K+] was fit 
with the Hill equation (Table II). Hill coefficients of 
∼1 suggest that one K+ ion interacts with the channel 
at a time, allowing permeation to be modeled as follows:
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\begin{equation*}K_{outside}^{+}+channel\begin{matrix}k_{1} \enskip  & \\ {\rightarrow}\; \enskip  & \\ {\leftarrow}\; \enskip  & \\ k_{-1} \enskip  & \end{matrix}[K^{+}bound\;to\;channel]\begin{matrix}k_{2} \enskip  & \\ {\rightarrow}\; \enskip  & \\ {\leftarrow}\; \enskip  & \\ k_{-2} \enskip  & \end{matrix}K_{inside}^{+}+channel.\end{equation*}\end{document} 


At high [K+] concentrations, saturation occurs when 
the rate of ion entry approaches the maximum rate of 
unbinding. For the BLM K+ channel, the maximum inward conductance (γmax = 34.3 pS) is voltage-independent, suggesting that at high concentrations of K+, the 
electrical driving force is the rate-limiting factor for ion 
flux. However, the binding-unbinding rate is voltage 
dependent, suggesting that the loading of the binding 
site for K+ is dependent on the membrane potential 
(Hille, 1992). Kawahara et al. (1987) also noted saturation of the Necturus BLM K+ channel conductance with 
external [K+] in c/a patches.

Voltage dependence.
Hyperpolarization increases nP
o. 
Such voltage sensitivity renders the channel susceptible 
to changes in membrane voltage, a potential regulator 
of the BLM K+ conductance. On the BLM in the Necturus proximal tubule, hyperpolarization increased K+ 
channel activity (Sackin and Palmer, 1987; Kawahara et 
al., 1987). In frog kidney, one study showed that nP
o increased with hyperpolarization (Kawahara, 1990), whereas 
in another study, no voltage dependence of nP
o was observed (Hunter, 1991). In preliminary experiments using rabbit proximal tubule, we again found that hyperpolarization increases nP
o, although Parent et al. 
(1988) reported the opposite. Note that for the cloned 
renal K+ channels, ROMK1 (Ho et al., 1993) and 
ROMK2 (Chepilko et al., 1995), which have not been 
detected in proximal tubule, nP
o decreases with hyperpolarization.

Selectivity and blockade.
The channel is highly selective 
for K+ over a number of cations (Na+, Rb+, Li+, NH4
+, 
and Cs+) as well as over Cl−. When K+ in the patch pipette was replaced by these cations, c/a and i/o 
patches failed to show inward channel currents. Paired 
experiments in outside-out patches show that gK:gNa exceeds 30:1, and that the cation selectivity of the BLM 
K+ channel is K+ >> Rb+ ≈ Cs+ ≈ NH4
+ > Na+ ≈ Li+ 
(see Fig. 5). Detailed selectivity data are lacking in 
other studies on BLM K+ channels in the proximal tubule, but more distal K+ channels, including ROMK, 
conduct Rb+. With Rb+ in the patch pipette, gRb/gK = 
0.36 for ROMK2 (Chepilko et al., 1995). Under similar 
conditions, we did not observe inward Rb+ currents 
through the BLM K+ channel.

Like other types of K+ channels (Hille, 1992), the 
BLM K+ channel can conduct thallium. Indeed, the 
single channel conductance is higher for Tl+ than it is 
for K+ (g*inTl/g*inK = 1.2). Since the reversal potential under biionic conditions (Tl+ pipette, K+ bath) is 
slightly positive, Tl+ is also more permeant than K+. 
This differs from ROMK2, in which Tl+ is also more 
permeant than K+ but the conductance for Tl+ is less 
than that for K+ (g*inTl/g*inK = 0.7) (Chepilko et al., 
1995). Thus, for the BLM K+ channel, Tl+ has a higher 
conductance and is more permeant than K+. 

Similar to other renal K+ channels, this BLM K+ 
channel is insensitive to tetraethylammonium. However, it is well known that the proximal tubule K+ conductance can be inhibited by millimolar concentrations of Ba2+ (Sackin and Boulpaep, 1981) and the 
whole-cell conductance of the dissociated Ambystoma 
cells is barium sensitive (Segal et al., 1996). Outside-out 
patches from the BLM show that K+ channel activity is 
inhibited by barium with a K
i of 460 μM at a command 
potential of −40 mV (see Fig. 7). Complete inhibition 
occurs at [Ba2+]o = 10 mM. 

Sensitivity to Nucleotides, Sulfonylureas, and Activation 
by Diazoxide
Nucleotides.
The Ambystoma BLM K+ channel is sensitive to ATP, albeit at millimolar levels. Since the first 
demonstration of an ATP-sensitive K (KATP) channel in 
cardiac muscle (Noma, 1983) and pancreatic cells 
(Cook and Hales, 1984), potassium channels inhibited 
by nucleotides have been described in a wide variety of 
tissues (Ashcroft and Ashcroft, 1990). In pancreatic β 
cells, KATP channels function in the regulation of insulin secretion. Ashcroft and Ashcroft (1990) have classified such inwardly rectifying KATP channels as Type I 
based on their exquisite sensitivity to ATP (K
i ∼ 10–100 
μM) and sulfonylureas. 

There is no doubt that KATP channels function primarily to couple cell metabolism to membrane potential 
(Ashcroft and Ashcroft, 1990), and perhaps to epithelial transport (Mauerer et al., 1998). Curiously, epithelial KATP channels appear to lack the exquisite sensitivity of Type I KATP channels, possibly for reasons discussed below. The proximal tubule BLM K+ channel 
described in this study is reversibly inhibited by ATP 
with a K
i of 2.4 mM at pH 7.5. This is a reasonable operating point given that intracellular ATP levels in proximal tubule are 4–5 mM, and ATP levels have been 
shown to fall to ∼2 mM when transport is stimulated 
(Beck et al., 1991; Tsuchiya et al., 1992). The role of intracellular ATP in coupling channel activity to pump 
turnover is discussed in the companion paper.

It is likely that the intracellular ATP-binding site contains a motif that recognizes a spectrum of nucleotides 
since the channel is also reversibly inhibited by GTP, 
ITP, UTP, CTP, and TTP (see Fig. 8
C). This putative 
binding site recognizes NTPs, NDPs, and NMPs, but 
not the nucleosides themselves. Adenosine nucleotides 
exert significantly stronger inhibition than their nonadenosine counterparts, and the triphosphate of a given 
nucleoside is a better inhibitor than the diphosphate 
and the monophosphate. Since the binding of NDPs 
and even NMPs is effective, channel inhibition probably does not require hydrolysis. In contrast to the KATP 
channel on the apical membrane of principal cells (Wang 
and Giebisch, 1991), the inhibitory effect of the nucleotides is probably not critically dependent on Mg2+ 
since nucleotide sodium salts (free Mg2+ ≅ 25 μM) are 
as effective as the magnesium salts (free Mg2+ ≅ 1.3 mM).

Sulfonylureas.
In cell-free patches, the Ambystoma and 
rabbit BLM K+ channels are (variably) inhibited by submillimolar levels of glibenclamide, whereas native cell 
Type I KATP channels are sensitive to nanomolar concentrations of glibenclamide (Ashcroft and Ashcroft, 
1990). Indeed, no renal and perhaps no epithelial K+ 
channel has the sensitivity to sulfonylureas (or ATP) 
that Type I KATP channels possess. This may suggest that 
either Type I KATP channels are only found in specific 
tissues, or that associated molecules (e.g., the sulfonylurea receptor) conferring sulfonylurea sensitivity are 
cell specific. In this regard, it is of interest that all but 
one of the cloned KATP channels fail to exhibit the degree of sulfonylurea sensitivity seen in the native β cell 
KATP channels. The exception is the KATP channel composed of Kir6.2 and the sulfonylurea receptor itself (Inagaki et al., 1995).

In the kidney, cloned ROMK channels are ATP regulated in the sense that they rundown in the absence of 
ATP, but also have a much lower (if any) sensitivity to 
ATP and sulfonylureas (Ho et al., 1993; Zhou et al., 
1994). At least on Northern analysis, the kidney also appears to lack SUR1 (Inagaki et al., 1995), which may 
partially account for the decrease in glibenclamide sensitivity. Of note, the renal K+ channel ROMK2 appears 
to be sensitive to glibenclamide when coexpressed with 
the cystic fibrosis transmembrane conductance regulator, but becomes much less sensitive after PKA phosphorylation of the patch (McNicholas et al., 1996). 
Since phosphorylation by PKA activates the BLM KATP 
channel (Mauerer et al., 1998), it may be that high current patches are already highly phosphorylated, and 
thus relatively insensitive to glibenclamide. That glibenclamide inhibition of the BLM KATP channel appears 
significantly more potent in cell-attached patches with 
smaller currents is consistent with this idea.

Diazoxide.
Diazoxide is a benzothiadiazine K channel opener (KCO) that activates several types of KATP 
channels. In many tissues, it is thought that activation 
by KCOs requires Mg-ATP (Edwards and Weston, 1993; 
Ashcroft and Ashcroft, 1990), as illustrated for the BLM 
K+ channel in Fig. 10. Diazoxide also does not alter the 
requirement for Mg-ATP to prevent BLM K+ channel 
rundown (see below). Indeed, diazoxide can be inhibitory in the absence of Mg-ATP, perhaps by accelerating 
channel rundown (Kozlowski et al., 1989). Therefore, 
it is not likely that diazoxide exerts its effect on the rundown site of the BLM K+ channel. 

For both the frog muscle KATP channel and the Ambystoma BLM K+ channel, KCOs lose their effectiveness 
at high (5–10 mM) intracellular [ATP]. This reciprocal 
effect on channel activity suggests a competitive interaction between KCOs and nucleotides. The activation 
by KCOs in the frog skeletal KATP channel is not Mg2+ 
dependent and, like the BLM K+ channel, does not occur in the absence of ATP. Further studies may thus 
show that diazoxide opens the BLM K+ channel by a 
mechanism similar to that recently proposed for KCO 
activation of the skeletal muscle KATP channel (Forestier et al., 1996).

Rundown of the BLM K+ Channel
A hallmark of KATP channels is that they exhibit the 
phenomenon of rundown, a gradual loss of activity 
when the membrane patch is deprived of cytosolic 
ATP. As first noted by Findlay and Dunne (1986), rundown is “a paradoxical situation in that K+ channels 
that are inhibited by intracellular ATP require intracellular ATP to retain the ability to open.” In a recent 
study on frog proximal tubule cells (Robson and 
Hunter, 1997), washout of intracellular ATP reduced 
the whole-cell barium-sensitive conductance by ∼60% 
over 10 min. Inclusion of 2 mM ATP in the patch pipette not only prevented this rundown, but the barium-sensitive conductance increased by 54% over 10 min. 

Accordingly, the BLM K+ channel runs down in the 
absence of ATP, and low concentrations of ATP (100–
200 μM) are required to prevent or rescue channel 
rundown in cell-free patches. Once rundown has begun, application of ATP will restore channel activity, 
but the ATP-restorable current decreases as the time 
between rundown and ATP application lengthens. The 
BLM K+ channel specifically requires Mg-ATP to support activity as rundown occurs if either ATP, Mg2+, or 
both are removed (see Table III). Typically, both Mg2+ 
and ATP are required to prevent rundown in KATP 
channels (Ashcroft and Ashcroft, 1990). Mg2+ is required as a cofactor, as channel rundown occurs in a 
Mg2+-free solution despite the presence of Na-ATP. 
Free Mg2+ concentrations as low as 200 nM are sufficient to prevent BLM K+ channel rundown in the presence of ATP. The possibility that free Mg2+ itself 
(rather than the Mg-ATP complex) plays a distinct role 
in the rundown of the BLM K+ channel cannot be excluded, but is difficult to test since rundown occurs if 
either Mg2+ or ATP is removed. Interestingly, free 
Mg2+ itself (≥10 μM) can prevent rundown of Kir2.1, 
an ATP-insensitive inward rectifier (Fakler et al., 1994).


Paradoxically, removal of free Mg2+ nearly abolishes 
rundown of KATP in cultured CRI-G1 insulin-secreting 
cells (Kozlowski and Ashford, 1990) and partially inhibits rundown of ATP-regulated ROMK1 channels excised in an ATP-free bath (McNicholas et al., 1994). 
The latter effect is presumed to occur via the inhibition 
of a Mg2+-dependent phosphatase (McNicholas et al., 
1994). Thus, removal of Mg2+ inhibits rundown in 
ROMK1, but actually produces rundown in the BLM 
K+ channel (see Fig. 9
C). We conclude that the Mg2+-dependent phosphatase thought to be involved in the 
rundown of ROMK1 (McNicholas et al., 1994) does not 
mediate rundown of the BLM K+ channel.

ATP can serve as a substrate in hydrolysis reactions 
mediated by an ATPase and in phosphorylation reactions mediated by a kinase. We asked whether phosphorylation itself (without hydrolysis) can prevent BLM 
K+ channel rundown, as has been proposed for other 
channels, including ROMK1 (McNicholas et al., 1994). 
To address this issue, we used ATP-γS, a poorly hydrolyzable ATP analogue that is an effective substrate for 
most kinases (e.g., PKA) in (thio)phosphorylation reactions (Eckstein, 1985). Similar to results reported for 
the cell KATP channel (Ohno-Shosaku et al., 1987), our 
findings (see Fig. 9 and Table III) indicate that ATP-γS 
cannot substitute for ATP in sustaining channel activity, whereas all hydrolyzable nucleoside triphosphates 
we tested do prevent or rescue rundown. The corresponding nucleoside diphosphates were also ineffective. 

In summary, rundown of the BLM K+ channel in excised patches seems to be prevented by a high affinity 
nucleotide binding site, which hydrolyzes nucleoside 
triphosphates in the presence of Mg2+. Rundown is 
prevented by ATP even in the presence of high concentrations of a protein kinase inhibitor, strongly suggesting that typical protein phosphorylation processes 
alone are insufficient to prevent/rescue channel rundown. Fakler et al. (1994) obtained similar results in 
Kir2.1 channels.

Comparison with Other Studies

Gögelein and Greger (1987b) found a very weak inward 
rectifier K+ channel on the lateral membrane of rabbit 
proximal straight tubule. In symmetrical KCl with 1 
mM Mg2+ in the bath, this channel had a limiting gin of 
∼45 pS and a limiting gout of ∼40 pS. In contrast to the 
results of the present study, their channel's open probability did not increase with hyperpolarization, and nP
o 
was unaffected by Ca2+ (<1 nM–1 μM) applied to inside-out patches (Mauerer et al., 1998). They did not 
observe channel rundown in excised patches, the channel was tetraethylammonium sensitive, and the effect of 
ATP was not tested. Thus, it is not likely that their channel was the BLM K+ channel we find in Ambystoma proximal tubule.


Kawahara et al. (1987) found a 31-pS K+ channel in 
42% of cell-attached patches made on the BLM of Necturus proximal tubule. They also found saturation of inward channel conductance at ∼50 pS (compared with 
∼35 pS for Ambystoma) and an apparent K
m of 65.5 mM 
(compared with 77 mM in Ambystoma). Whereas we observed inward rectification for all [K], their I-V plots 
were restricted to inward currents. Similar to our findings in Ambystoma, the K+ channel in Necturus showed 
high selectivity (PK:PNa ≈ 10:1 in Necturus versus ≈ 30:1 
in Ambystoma), channel activity increased with hyperpolarization, and external Na+ did not influence channel 
behavior. They also found that hyperpolarization did 
not affect channel open time; rather, the increase in 
nP
o was due to shortening a closed state lifetime. Significantly, Kawahara et al. (1987) were unable to maintain 
channel activity in excised patches, stating that “patches 
became unstable and noisy after excision.” It is likely 
that this was channel rundown since this description is 
reminiscent of the channel “choking” and rundown we 
observe in an ATP-free bath. 

Similarly, Sackin and Palmer (1987) observed two 
BLM K+ channels in Necturus, a short open-time channel that they studied in detail, and a long open-time 
channel that disappeared after excision, perhaps because of rundown. The short open-time channel is different from the BLM K+ channel of Ambystoma since it 
was nonrectifying and did not rundown when excised 
in an ATP-free bath. The long open-time channel was 
thought to be the same as that studied in cell-attached 
patches by Kawahara et al. (1987), and probably corresponds to the BLM K+ channel in Ambystoma except the 
channel in Necturus had a mean open time of ∼60 ms, 
much longer than that seen in our study. 


Parent et al. (1988) made cell-attached patches on 
rabbit BLM and found an inward-rectifier K+ channel 
that had different properties than both the Ambystoma 
BLM K+ channels in the present study. Their voltage 
dependence was opposite to ours, as they concluded 
that hyperpolarization induced a long closed state.


Hunter (1991) made cell-attached patches on the 
BLM of single frog proximal tubule cells and found 
only one kind of K+ channel, an inward rectifier with 
an inward gslope = 32.4 pS, and an outward gchord = 6.2 
pS at +80 mV, similar to the one we studied on the 
BLM of Ambystoma proximal tubule. Depolarization reduces the macroscopic BLM K+ conductance and single-channel conductance in both preparations. A Boltzmann fit of the g–V curves (rederived using Fig. 5 of 
Hunter, 1991, and the inset of Fig. 3
B in the present 
study) shows a V1/2 = +31.7 mV and a width of 14.5 mV 
for the BLM K+ channel in c/a patches of frog, compared with a V1/2 = −14.9 mV and a width of 21.3 mV 
for the BLM K+ channel in i/o patches of Ambystoma. 
Thus, the sensitivity of conductance versus voltage is 
such that there is an e-fold change in g per 14.5 mV in 
frog (c/a), and per 21.3 mV in Ambystoma (i/o). The 
discrepancy in V1/2 may be due to different experimental conditions and levels of cytosolic Mg2+. Hunter 
(1991) also reported that the addition of glucose and/
or alanine did not affect BLM K+ channel activity in the 
frog cells. Although addition of alanine depolarized Vm > 30 mV, he was unable to explain the repolarization 
of the BLM under his experimental conditions. In contrast, the Ambystoma BLM K+ channel under discussion 
is activated by these substrates, which can explain the 
repolarization of the BLM (Mauerer et al., 1998). In a 
recent follow-up study, Robson and Hunter (1997) proposed that, based on differential sensitivity to barium 
and quinidine, the frog cells have two separate K+ conductances. The inwardly rectifying conductance that 
was inhibited by both agents appears similar to the Ambystoma BLM KATP channel, although direct sensitivity 
to ATP or glibenclamide was not tested in their study.


Tsuchiya et al. (1992) found an ATP-sensitive K+ 
channel in five patches made on the BLM of nonperfused rabbit S1 and S2 segments. With 145 mM K+ in 
the patch pipette and a bath containing 140 mM Na+ 
and 5 mM K+, they reported an inward gslope = 56 pS, 
although an I-V plot was not given. In c/a patches at a 
command potential of 0 mV, they found a baseline nP
o 
of 0.72, much higher than that found in the present 
study and the two studies in which perfused tubules 
were patched (see below) (Hurst et al., 1993; Beck et 
al., 1993). Although 1 mM ATP applied to the cytoplasmic side of an inside-out patch reversibly reduced nP
o 
by 77% (from 0.70 to 0.16), the sensitivity of the basolateral conductance was reduced in a perfused tubule 
when 1 mM ATP was added to the bath.


Beck et al. (1993) were the first to patch clamp the 
BLM of (collagenase-treated) perfused rabbit proximal 
tubules, and found a K+ channel whose activity correlated to transport activity. This channel showed inward 
rectification in c/a patches (with gin = 61 pS and gout = 
17 pS) and P
o was voltage independent. In a follow-up 
study (Hurst et al., 1993), the same group showed that 
2 mM ATP (i/o) inhibited channel activity by ∼80% 
and 100 μM diazoxide (c/a) effectively opened this 
BLM K+ channel.

The ROMK family of K+ channels is, to date, the only 
cloned ATP-regulated renal K+ channel (Ho et al., 
1993). The ROMK1 channel cloned from rat kidney is 
an inwardly rectifying K+ channel with gin = 39 pS and 
a high open probability (0.8–0.9) at voltages more depolarized than −60 mV, and is not activated by hyperpolarization. ROMK1 exhibits channel rundown when 
membrane patches are excised in ATP-free bath, although ROMK1 is not sensitive to ATP or glibenclamide (Ho et al., 1993). In situ hybridization studies 
show that transcripts (mRNA) for ROMK are absent 
from the proximal tubule (Lee and Hebert, 1995). 
Combined with the differences in mechanism of channel rundown (see above and Table III), it is highly unlikely that the BLM K+ channel is ROMK1, although it 
may be within the same family of inwardly rectifying K+ 
channels with two transmembrane domains (Ho et al., 
1993; Kubo et al., 1993).

Contribution of the BLM K+ Channel to Total 
BLM Conductance
The component of BLM conductance (GBLM) due to 
the BLM K+ channel (GK) can be estimated as:
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\begin{equation*}G_{K}=\frac{g{\cdot}nP_{o}{\cdot}f}{a},\end{equation*}\end{document} 


where g is the “physiologic” single channel conductance, n is the average number of channels in a patch, 
P
o is the mean open time of one channel, f is the incidence of finding a channel in the patch, and a is the 
area of the membrane patch. 

In the present study, the conductance (g) for outward currents was ∼4 pS, the average nP
o extrapolated 
to 0 mV was 0.20, and channel activity was found in 
98.6% of patches. Given that the average inner diameter of our patch pipette was 1.5 μm, the minimal membrane area of a patch is 1.77 μm2. Using these estimates 
in Ambystoma, the value for GK is (4 pS*0.20*0.986)/
1.77 μm2 = 0.446 pS/μm2 or 44.6 S/cm2 (RK = 22.4 kΩ · 
cm2). Considering the estimate of GBLM = 51.3 μS/cm2 
(RBLM = 19.5 kΩ · cm2) in Ambystoma proximal tubule 
(Maunsbach and Boulpaep, 1984), GK/GBLM = 44.6/
51.3 = 0.87. Thus, under the conditions used in our experiments, GK may account for 87% of GBLM. However, 
to the extent that the area of the membrane patch is 
larger than our estimate, GK will be smaller. 

The basolateral membrane area of dissociated Ambystoma proximal tubule cells exhibits less infoldings 
than these cells in situ (Segal et al., 1996). Assuming a 
whole-cell membrane capacitance of ∼120 pF (Segal et 
al., 1996) and a specific capacitance of 1 pF per 100 
μm2, we can estimate that the surface of a single isolated cell is ∼12,000 μm2. Using a BLM surface area of 
10,000 μm2 (100 × 10−6 cm2) and a GBLM = 51.3 μS/
cm2, the total BLM conductance is 5.13 nS. Using the 
transport number GK/GBLM of 0.87 from Table IV, GK 
= 4.46 nS. Despite possible changes in membrane area 
(e.g., due to membrane recycling) and/or channel 
density that could occur in the dissociated cells over 
time, this is a reasonable estimate since perforated-patch whole-cell studies with KCl pipette and NaCl bath 
(EK = −84 mV) show current that reverses at Vm = −40 
mV with ∼240 pA of outward current at 0 mV command potential, and a whole-cell conductance of 6 nS. 
Thus, the total BLM conductance is 5.13 nS, of which 
4.46 nS is K conductance, and the total apical conductance is 0.87 nS (the difference of 6–5.13). 


Similar comparisons between GK derived from single-channel data and GBLM based on cable analysis are 
shown in Table IV for Necturus, Rana, and rabbit proximal tubule, respectively. With the exception of the rabbit, the transport numbers show that the BLM conductance of all other species is dominated by K+ and, 
specifically for Ambystoma, KATP channels. From this information, one can estimate the K+ channel density on 
the BLM of dissociated Ambystoma proximal tubule 
cells. If P
o was unity, the number of channels would be 
given by 4.46 nS/4 pS = 1,115 channels. However, 
since P
o = 0.05, the number of K+ channels on the 
BLM is ∼22,300 per cell; a channel density of 2.23 
channels/μm2. Using the estimate of membrane patch 
area of 1.77 μm2, one would expect on average approximately four channels per patch, in good agreement 
with our experience.

Physiological Role of the BLM KATP Channel
The task of the proximal tubule under physiologic conditions is to effect transport; i.e., to maintain ionic flux 
in the direction of reabsorption. The electrochemical 
difference across the BLM of proximal tubule, given by 
Vbl − EK, is an invariably positive driving force promoting K+ efflux (Boulpaep, 1979). The presence of other 
conductances in the BLM with reversal potentials less 
negative than EK provides a nonzero difference between EK and Vbl that maintains K efflux. The BLM 
Na+,K+-ATPase pump loads the cell with two K+ ions to 
effect the transcellular transport of three Na+ ions. An 
efflux pathway for K+ is necessary to recycle K+ across 
the BLM, thus permitting continuous operation of the 
pump. Pump activity and the opening of these K+ channels hyperpolarize the BLM, favoring apical Na+ entry. 
An interesting contrast is that the negative shift in 
membrane potential consequent to the opening of 
KATP channels tends to depress cell function in excitable cells, but tends to promote transport in epithelia. 
The magnitude of BLM K+ efflux must match the K+ 
current of the pump. The regulatory effects of hyperpolarization and intracellular ATP levels on the BLM 
KATP channels thus subserve this role.

This system of a variable BLM K+ conductance coupled to changes in pump rate in a single cell has further implications when extrapolated to the level of an 
epithelium with a paracellular shunt pathway. Such an 
epithelial model should include all current pathways 
(see Fig. 11, adapted from Fig. 5 of Sackin and Boulpaep, 1983); namely, (a) the active Na+ and K+ pump 
currents, (b) the basolateral K+ leak current, (c) the 
other basolateral leak currents, principally carried by 
Cl−, and (d) the shunt current carried by Cl− and, to a 
lesser extent, by Na+. In this equivalent electrical cell/
circuit, Kirchoff's current law at node A gives
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\begin{equation*}I_{net}^{pump}+I_{K}^{bl}-I_{Cl}^{bl}-I_{total}^{shunt}=0,\end{equation*}\end{document} 


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\begin{equation*}I_{net}^{pump}=I_{Na}^{pump}-I_{K}^{pump},\hspace{.167em}I_{K}^{bl}=(V_{bl}-E_{K}){\cdot}G_{K}^{bl},\hspace{.167em}I_{Cl}^{bl}\end{equation*}\end{document}
is 
the transcellular component of Cl− absorption, and 
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\begin{equation*}I_{total}^{shunt}=I_{Cl}^{shunt}+I_{Na}^{shunt}\end{equation*}\end{document}
(i.e., the sum of the paracellular 
component of Cl− absorption and any Na+ backleak). 
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be exactly matched to \documentclass[10pt]{article}
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\begin{equation*}I_{K}^{pump}\end{equation*}\end{document}
, then Eq. 11 becomes 
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\begin{equation*}I_{Na}^{pump}-I_{Cl}^{bl}-(I_{Cl}^{shunt}+I_{Na}^{shunt})=0.\end{equation*}\end{document} 


When Eq. 12 is satisfied, all actively transported Na+ 
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\begin{equation*}I_{Na}^{shunt}\end{equation*}\end{document}
. Under these optimal conditions, the proximal tubule accomplishes NaCl reabsorption at maximum efficiency.

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\begin{equation*}G_{K}^{bl}\end{equation*}\end{document}
did not increase with pump rate, \documentclass[10pt]{article}
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\begin{equation*}I_{K}^{bl}\end{equation*}\end{document}
would rise only slightly due to the small increase in 
driving force. Under these conditions, \documentclass[10pt]{article}
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\begin{equation*}I_{Na}^{pump}{\textgreater} I_{Cl}^{bl}+\;\end{equation*}\end{document}
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\begin{equation*}(I_{Cl}^{shunt}+I_{Na}^{shunt})\end{equation*}\end{document}
and the efficiency of NaCl reabsorption 
deteriorates. That is, the incremental increase in NaCl 
reabsorption would be less than that of the pump. 
Therefore, the tight linkage between the Na+,K+-ATPase pump and the K+ leak through the BLM KATP channels is especially important in leaky epithelia that absorb large, fluctuating quantities of NaCl such as the 
proximal tubule. The regulation of the BLM KATP channels and how they are coupled to the pump during 
transport is the subject of the companion paper 
(Mauerer et al., 1998).

This work was supported by grant DK-17433 from the National Institutes of Health (NIH). Dr. A. Segal is a recipient of a 
Physician-Scientist Award from the NIH (DK-02103). 

This work is dedicated to the memory of Dr. Roman Mauerer (father of Ulrich Mauerer), who passed away during the preparation of the manuscript. The authors thank Ms. Christine Macol for excellent technical assistance. 

1 
Abbreviations used in this paper: BLM, basolateral membrane; c/a, 
cell-attached (patch); I-V, current–voltage; i/o, inside-out (patch); 
KCO, K channel opener; nP
o, channel activity represented as the 
product of the minimum number of channels (n) times the open 
probability (P
o) of the channel; SUR, sulfonylurea receptor.

Table I Solutions

		
a
NaCl
Ringer		
b 
Ca2+/Mg2+-
free Ringer		
c 
NaCl recording
solution		
d 
KCl recording
solution		
e 
Mg-free
KCl		
f 
KCl 200 nM
Mg2+
		
g 
Tl+ pipette
solution		
h 
2 mM Cl−
K solution		
i 
KCl salt
dilution	
Na+
		 95.9		 98.5		 95		  2.5		  2.5		  2.5		  5				  2.5	
K+
		  2.5		  2.5		  2.5		 95		 95		 95				 95		 14	
Cl−
		 98.1		 92.5		 94.5		 94.5		 92.5		 96.1		  2		  2		 13.5	
Ca2+
		  1.8																	
Mg2+ 
(added, mM)		  1				  1		  1				  0.81		  1		  1		  1	
Mg2+ 
(free, nM)												200							
Tl+
														 90					
Acetate−
														 90		 90			
HEPES		  5		  5		  5		  5		  5		  5		  5		  5		  5	
HEPES−
		  5		  5		  5		  5		  5		  5		  5		  5		  5	
EGTA						  1		  1						  1		  1		  1	
EDTA				  1		  		 		  8		  8		  		 		  	
H2PO4
−
		  0.1		  0.1															
HPO4
2−
		  0.4		  0.4															
Dextrose		  2		  2															
pH (titrand)		  7.5
(NaOH)		  7.5
(NaOH)		  7.5
(NaOH)		  7.5
(KOH)		  7.5
(KOH)		  7.5
(KOH)		  7.5
(NaOH)		  7.5
(KOH)		  7.5
(KOH)	
Osmolality		200		200		200		200		200		200		200		200		200	
Figure 1 Dissociated Ambystoma 
proximal tubule cells retain epithelial cell polarity. (A) Light photomicrograph of a single dissociated Ambystoma proximal tubule 
cell shows distinct apical and basolateral membrane surfaces. The 
apical surface of these bilobated 
cells is the smaller lobe with a microvillar brush border. The robust 
cytoskeleton of these cells includes an actin-rich “waist-band” 
(arrowheads) between the two 
membrane domains that is important in retention of epithelial 
polarity. Giga-ohm seals can be 
made on both surfaces. Scale bar, 
10 μm. (B and C) Scanning electron micrographs showing the 
sharp transition between the 
membrane domains and the detailed topology of the apical surface invested with its microvillar 
brush border, and the basolateral surface with its folds and 
projections. Scale bars: 10 μm in 
B, 1 μm in C.

Figure 2 The BLM K+ channel appears to be an inward rectifier. (A) Representative current records at various command potentials 
(−Vpip) from a cell-attached basolateral membrane patch containing at least two K+ channels. Note the increase in channel activity with hyperpolarization. The patch pipette contains 95 mM K+ (solution d) and the bath is NaCl (solution c). The dashed line represents the all 
channels closed (leak) current at each potential. Each open channel level is denoted by a dotted line. (B) Current–voltage relation for the 
BLM K+ channel for the conditions described in A. The limiting inward slope conductance is 22.2 ± 1.4 pS (n = 8) and the outward chord 
conductance 3.5 ± 0.1 pS (between 120 and 180 mV, n = 5). Symbols represent mean (•) ± SEM (bars).

Figure 3 The BLM K+ channel is a true inward rectifier. Representative current records at various command potentials (−Vpip) from an 
inside-out basolateral membrane patch in symmetrical [K] containing at least three K+ channels. The patch pipette and bath each contain 
95 mM K+ (solution d) with 0.2 mM ATP added to the bath. The dashed line represents the all channels closed (leak) current at each potential. Each open channel level is denoted by a dotted line. (B) Effect of [Mg2+]i on the I-V relation of the BLM K+ channel. The inward 
rectification evident in 1 mM [Mg2+]i (○) is relieved when [Mg2+]i is lowered to 200 nM (▪). (inset) Slope conductance–voltage (g-V) relation for the BLM K+ channel in 1 mM [Mg2+]i (○) and 200 nM [Mg2+]i (▪). Symbols represent mean ± SEM. The K+ channel prefers Tl+ 
over K+. The I-V relation from inside-out patches with Tl-acetate (solution g) in the pipette and K-acetate (solution h) in the bath is also 
shown (▴). The limiting inward slope conductance is 29.0 ± 1.0 pS (n = 4) for Tl+ compared with 24.5 ± 0.6 pS (n = 8) for K+. (C) Channel activity (nP
o) increases with hyperpolarization. Data from four inside-out membrane patches in symmetrical [K] are plotted. Channel 
activity at command potentials of −120, −100, −80, −60, and −40 mV was normalized to that at −100 mV for comparison. Solid line is a 
single exponential fit with a voltage constant of ∼83 mV. Symbols represent mean (•) ± SEM (bars).

Figure 4 The operating surface of the BLM K+ channel. (A) 
The single channel conductance (γ) at a command potential of 
−100 mV plotted as a function of [K+] and fit to the Hill equation 
according to \documentclass[10pt]{article}
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\begin{equation*}{\gamma}={\gamma}_{max}{\cdot}[1+(K_{d}/[K^{+}]_{o})^{n_{H}}]^{-1}{\cdot}{\gamma}_{max}\end{equation*}\end{document}
is the maximal value of the conductance, K
d is the apparent dissociation constant, and n
H is the Hill coefficient. For the chord conductance at 
−100 mV (▪) and its least-squares fit (solid line), γmax,slope = 34.3 
pS, K
d = 77 mM, and n
H = 0.94. (B) The plot of K
d versus Vpip 
shows that the apparent binding–unbinding rate of K+ to the 
channel is voltage dependent. The data (○) were fit with a single 
exponential (solid line) as follows: K
d = 73 + 141 · exp(−Vpip/30).

Table II Kd Values and Hill Coefficients for the BLM K+ Channel

Command potential		
K
d
		Hill coefficient	

mV
		
mM
		
nH
	
−20		146		0.94	
−40		110		1.02	
−60		 92		0.96	
−80		 85		1.00	
−100		 77		0.95	
Figure 5 The BLM K+ conductance is highly selective for 
K+. The cationic selectivity of the 
BLM is demonstrated in this outside-out patch with KCl (solution d) + 0.2 mM ATP in the pipette and Cl-salt of the test cation 
in the bath. The running average 
of current at −40 mV shows that 
cationic selectivity is K+ >> Rb+ 
≈ Cs+ ≈ NH4
+ > Na+ ≈ Li+. The 
dashed line is the zero-current 
line, and the dotted line is the all 
channels closed (leak) current at 
a command potential of −40 
mV. The voltage protocol is indicated below the current data.

Figure 6 Kinetics of the BLM K+ channel. (A) Open-time histogram for the BLM K+ channel in a cell-attached patch at −60 mV 
with the time intervals logarithmically binned (Sigworth and Sine, 
1987). The data were fitted with two probability density functions 
(dashed lines) to give the overall fit (solid line), yielding time constants of τo1 = 0.78 ms (78%) and τo2 = 4.7 ms (22%). Based on 
the bandwidth of the recording system, the data and the fit were 
cutoff at 500 μs (vertical dotted line). (B) Closed-time histogram for 
the BLM K+ channel in a cell-attached patch at −60 mV with the 
time intervals logarithmically binned. The data were fitted with two 
probability density functions (dashed lines) to give the overall fit 
(solid line), yielding time constants of τc1 = 1.27 ms (74%) and τc2 
= 397 ms (26%). Based on the bandwidth of the recording system, 
the data and the fit were cutoff at 500 μs (dotted vertical line).

Figure 7 Inhibitors of the 
BLM K+ channel. (A) Dose–
response curve for inhibition of 
the BLM K+ channel by external 
Ba2+. Relative nP
o (nP
o/nP
o,control) 
determined from outside-out 
patches at a command potential 
of −40 mV with KCl in the pipette and bath (solution d) is 
plotted versus [Ba2+]. The data 
at −40 mV were fitted with the 
Hill equation (solid curve), yielding a K
i = 460 μM and n
H = 0.90. 
The inhibition by Ba2+ is fully reversible. (B) Glibenclamide inhibits the BLM KATP channel. 
(top) A running average (window 
width 16 ms) of current versus 
time. Glibenclamide (500 μM) is 
added to the bath where indicated. (bottom) Sample traces 
from a representative experiment at −60 mV with KCl in the 
pipette and bath (solution d). Exposure of this inside-out patch to 500 μM glibenclamide reversibly decreases nP
o by ∼50%. The dashed line denotes the all channels 
closed (leak) current level and the dotted lines indicate each open channel level.

Figure 8 Nucleotides reversibly inhibit the BLM K+ channel. (A) ATPi reversibly inhibits the BLM K+ channel in inside-out patches. In 
the experiment depicted, up to 13 channel open levels are seen under control conditions (top) at −60 mV with KCl (solution d) in the pipette and NaCl (solution c) plus 0.2 mM ATP in the bath. (middle) Addition of 5 mM ATP to the cytoplasmic side almost completely blocks 
channel activity (98% decrease) with only rare openings to one open level. (bottom) The inhibition is readily reversed upon returning to 0.2 
mM ATPi. (B) Dose–response curve for inhibition by ATPi. The inhibitory effect of ATPi was determined in inside-out patches under the 
conditions described in A. Relative nP
o (nP
o/nP
o,control) is plotted versus [ATP]i. The data (•) was fitted with the Hill equation (solid line) 
yielding a K
i ∼ 2.4 mM and n
H = 3.95. Adenosine nucleotides and nucleoside triphosphates (each at 5 mM) inhibit the BLM K+ channel. 
The inhibitory effect of ATP, ADP, AMP, and adenosine was determined under the conditions described in A. Values plotted are average 
(nP
o,test/nP
o,control) SEM (n = 3–9). The rank order of inhibition is ATP (93.3%) > ADP (65.6%) > AMP (38.7%). Adenosine has no inhibitory effect on nP
o of the BLM K+ channel. Although all the nucleoside triphosphates inhibit the channel, ATP exerts a significantly stronger block than the other NTPs tested (P < 0.02). There is no significant difference among the other NTPs.

Figure 9 ATP but not ATP-γS prevents and rescues channel rundown. Hydrolyzable nucleoside triphosphates prevent and rescue BLM 
K+ channel rundown. A running average (current versus time, window width 768 ms) of a representative experiment is shown. The pipette 
is KCl (solution d), the bath is NaCl (solution c), the command potential is −60 mV. Upon excision in a nucleotide-free bath, channel activity decreases (channel rundown). After the addition of 0.2 mM ATP to the bath, channel activity slowly recovers. The addition of 0.2 mM 
ATP-γS (a poorly hydrolyzable ATP analogue) in the continued presence of 0.2 mM ATP has no effect. However, when ATP is removed, 
ATP-γS is not able to support channel activity, which rapidly declines and runs down. Readdition of ATP leads to full recovery of channel 
activity. Single-channel traces showing that ATP-γS has an inhibitory effect on KATP channel activity in excised inside-out BLM patches. 
When compared with control conditions (top), the addition of ATP-γS (middle) reduces nP
o. This inhibition is reversible as long as the exposure to ATP-γS is not prolonged (bottom). (C) Removal of Mg2+ does not prevent channel rundown in an ATP-free bath. The top panel 
shows that rundown of the BLM KATP channel upon excision into an ATP-free bath proceeds despite removal of bath Mg2+. Representative 
traces from the regions marked by α, β, and γ are shown at bottom. 

Figure 10 The K channel opener diazoxide activates the BLM K+ channel. Diazoxide activates 
the BLM K+ channel in the presence of ATP. In 
the experiment depicted, the pipette contains 
KCl (solution d), the bath contains NaCl (solution 
c), and the command potential is −80 mV. (top) A 
running average (window width 16 ms) of current 
versus time. (bottom) Sample current traces from 
the same experiment. With diazoxide alone, the 
channel opens infrequently (nP
o = 0.15) and no 
more than two channels are open at a time. Diazoxide combined with 0.2 mM ATP, however, 
promptly increases channel activity and within 5 
min, up to 13 simultaneously open channels are 
evident (nP
o = 5.27). The all channels closed 
level (dashed line) and open channel levels (dotted 
lines) are indicated.

Table III Rundown for ROMK1 Compared with the BLM K+ Channel

Nucleotide		Free Mg2+
		ROMK1
rundown*
		BLM K+
rundown	
0.2 mM ATP		1 mM Mg2+
		No		No	
0.2 mM ATP-γS		1 mM Mg2+
		?		Yes	
ATP-free		1 mM Mg2+
		Yes		Yes	
0.2 mM ATP		Mg2+-free		Yes		Yes	
ATP-free		Mg2+-free		No		Yes	
*  As expressed in Xenopus oocytes; data from McNicholas et al. (1994).
 

Table IV Contribution of the K+ Conductance to the BLM Conductance of 
Proximal Tubule

Species		g		NPo
		f		A		GK
		GBLM
		GK/GBLM
	
		
pS
						
10−8cm2
		
μS/cm2
		
μS/cm2
			

Necturus
		31.2*
		0.14*
		1.0*
‡
		1.3*
		 33.6*
		33–59§
		0.57–1.00	
						0.42*
				 14.1				0.24–0.43	

Rana
		 5.6‖
		0.22‖
		0.62‖
		1.57‖
		 48‖
		33–59§
		0.81–1.45	
												 51.3¶
		0.94	
Rabbit		10**
		0.06**
		1.0††
		1.0**
		100**
		714§§
		0.14	

Ambystoma
		 4‖‖
		0.20‖‖
		0.986‖‖
		1.77‖‖
		 44.6‖‖
		 51.3¶
		0.87	
*  From Kawahara et al., 1987; cell-attached at 0 mV;  

‡  assumed in the calculation in Kawahara et al. (1987), despite finding f = 0.42;  

§  from 
Maunsbach and Boulpaep (1984), for Necturus;  

‖  from Hunter (1991), cell 
attached at 0 mV;  

¶  from Maunsbach and Boulpaep (1984), for Ambystoma;  

**  from Parent et al. (1988), cell-attached at −50 mV;  

††  presumed, since 
data not given in Parent et al. (1988);  

§§  from Lapointe et al. (1984);  

‖‖  present study.
 

Figure 11 Equivalent electrical cell/circuit. Adjacent proximal tubule cells are outlined as 
dashed lines, and the equivalent 
circuit discussed in the text is diagrammed on the left. The basolateral membrane potential is denoted by voltage source Vbl. The 
current produced by the Na,K-ATPase pump, Inet
pump is given by 
INa
pump + IK
pump. Basolateral ion 
channel currents are shown as 
their Thévenin equivalents with 
their conductances, GK
bl and 
GCl
bl, represented by the equivalent resistor, in series with their 
Nernst potentials, EK and ECl, respectively. The paracellular current, Itotal
shunt is represented by 
INa
shunt + ICl
shunt. RA is the resistance of the apical membrane. 
Kirchoff's current law at Node A 
is given by Eq. 11.
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